The internet exposes us to a wide array of perspectives, beliefs, and behaviors that we might not encounter in our immediate, offline environments.
We are outraged by this.
Maybe this is our lizard-brain threat detectors tuned to primitive local survival requirements. An existence where the number of people and places you will encounter in 50 years of life expectancy can be tallied on your fingers. If our ancient white blood cells see modern connectivity as an intruder, our system 2 reasoning can be used to restrain that impulse…”chill sentry, these other ways of being were always there, we just didn’t see them before”.
There’s a particular brand of discourse that recurs constantly on #fintwit’s personal finance channels. It goes like this:
Original poster: “I need this much to retire”
Someone is 100% to be offended and responds:
“No you don’t because [reasons]”
This is a surefire way to farm engagement. It’s a close cousin to NY Times favorite style of finance article “I make $1mm a year and can’t afford life”.
Here’s Ramit, whose personal finance content I usually like, playing the game:
Everyone’s entitled to their opinion. I find it difficult to get emotional or even conjure opinions on such a topic. It’s an impotent path of inquiry because it is absolutely crushed by the sheer magnitude of how our perceptions emerge from limitless forking paths of human experience.
I just short-circuit at normative questions of “what should be”. Feels arrogant to get riled up about what others think they need. We change. If you grow up with little and do well, your sights will get set higher. Is this bad? Seems like the wrong question. A misdirection from a more useful framing. And that framing is also a matter of opinion. But that’s one I have a view on.
To invite a personal perspective I’ll admit a simplistic desire. When it comes to what I want to afford, I wanna live in a nice town in CA and not have to count my pennies in the course of a comfortable existence. One in which a special occasion stay at 5 star hotel doesn’t require a separate savings account. But I don’t expect to have a yacht or live-in maid.
At the same time, I don’t pretend we can’t have a lost decade or 2 of returns. It might be low probability but you don’t need to catastrophize to think it’s part of the distribution. Relying on even historical assumptions of investment returns feels uncomfortably fragile to me. Life is a single draw. Relying on non-stationary averages is a building a house like the first 2 little piggies.
[Note: This asset management marketing pitch called “evidence-based investing” offers useful heuristics but if it over-loads your “extrapolate from the past” muscle it’s a Trojan Horse.]
My no-shortcuts belief:
Find the mix of work and expectations that give you a chance of getting to a number with a very high margin of safety which is always going to look like a big number. But you don’t make your happiness contingent on getting there.
My rebuttal to all these “you can get retire on as little as X” is sure you can go live in Egypt too for even less. Maybe I need X because I be living like Y. And it takes a lot of arrogance to yuck people’s Ys. It’s possible they have distorted goggles on but, unless they want help, to assume they are broken feels like a strange position. The American who needs 20mm to retire vs the person who needs 1mm.
Does it really take that much effort to imagine either person without thinking one of them is crazy? You won’t unsee it once I say it — arguing over ranges where reasonable people can disagree is the gasoline of the internet.
The whole “what you need” discourse is a distraction from the plain truth — there is an “arrival” fallacy at play. It’s very well documented across the board. Win the championship, celebrate one night, then feel letdown. Living in the future (or past) sucks. Never overdose on hope or nostalgia.
So that bloke that gets to 15mm and won’t stop “until he gets 25” is probably wrong on thinking there’s an endpoint.* But calling him out for his mentality is judgmental at best and wrong at worst. Maybe that mentality was a prereq to getting to 15 in the first place. Every strength is also a weakness (or so I tell myself when I forget to buy milk because I was daydreaming).
*I don’t think about a “number” because if you hit it you still have to contend with what you’d do with your time. You should stop pretending that is a problem you acquire when you “arrive”. You have that problem right now.
Instead, we can choose grace and not think unusual people need fixing (again unless the person is seeking help). Should posters just write a boilerplate disclaimer: “I realize it’s gauche to say I want 25mm to retire and any reasonable person could retire on less but…”? Do they need to splay themselves on the altar of “be considerate to the average human” before speaking?
There are subgroups of people that, for better or worse, have their own standards for how they want to spend their revolutions around the sun. We could simply choose rules of charitable engagement to assume that default belief instead of compressing variation. When someone posts on r/FatFire they are talking to a selected group of mutuals. You know what’s going to happen when you paste that in the internet’s town square.
My wife and I come from middle to lower class families. Yet, because of our professions have seen a lot of how the other half lives. And we’re part of the other half as our childhood selves would conceive of it. I thought any kid with a GI Joe aircraft carrier was rich. My wife’s “this person must be rich moment” was when she had dinner at a friend’s house and they had Ranch dressing. I only have to drive around my town to know there’s “another half” compared to our current perspective. And to them there’s “another half” flying private everywhere. You get the point.
Not relating to someone else is not news. It’s what should be expected because of how wide the range is. How can something that shouldn’t surprise you, get you fired up? The whole discourse is low-brow projection.
Here’s an experiment to undo this impulse. Consider the Guinness Book. Longest fingernails? Is there any point in trying to relate to someone who goes for that. We don’t try because it’s absurd. The range of humanity is blindingly obvious when you turn those pages.
But when people start talking about money (as opposed to their time, which Guinness people used in wild ways) we somehow think that should be more relatable. Resist that illusion.
You don’t need worry about what everyone wants. These are not matters of right and wrong (vs the boring problem of someone making the equivalent of a counting mistake in describing the how of their money pursuits).
You need $100mm, cool. You wanna live in a van. Right on. For all I hope your expectations are met.
But I don’t think that’s how anything works. Solving for the best way to be useful and happy is a lifelong endeavor. It’s not where you are gonna eventually plant your flag it’s how you carry its weight every day.
It’s true and forgiving to recognize that a lot of people don’t have the luxury of the thought — but what’s much worse is how many don’t have the nerve.
Last week in Breakpoints, the discussion was about measuring implied skew.
A common measure and the one we use in moontower.ai is normalized skew which computes the percent premium or discount of IV at the 25d strike vs the 50d strike.
It’s not a measure that lends itself to direct interpretation. If 50d IV is 30% and the 25d put is 36% that’s a normalized skew of 20%. It doesn’t mean anything on its own but it is useful to see if skew is relatively or historically high or low. You chart it as a time series or percentile the value on a 1 or 2 year lookback. You can compare skew cross-sectionally across correlated assets.
Skew, or any measure, can be attacked from any number of angles. Our single measure of normalized skew itself requires choosing tradeoffs. The last post addressed the biases of various breakpoints. Moneyness, standard deviation, and delta-relative are all common ways to fix the gridpoints.
Today, we’ll use an approach that many might find more intuitive — thinking about skew in terms of option premiums instead of implied vol. When we look at option chains we are looking at prices. When we trade options our p/l depends on how the premiums change. For many investors, premiums are a more natural way to think about options than IV.
We will use GME to demonstrate a number of ways to think about skew which are more tightly intertwined with how skew trades are expressed — through verticals and ratio’d verticals.
We can even turn the metrics into a simple oscillator based on arbitrage bounds. If I do my job right, this post will make the concept of skew more concrete and inspire you to track it in new ways.
I started this GME case on a data exploration lark. Baycrest option strategist David Boole said that the call skew on the latest rally surpassed even the 2021 craziness. I wanted to look myself but I didn’t want to just look at normalized skew by delta.
Because I knew the call skew was so fat I was a bit uneasy about the recursive nature of delta-relative gridpoints. The last post uses a concrete example to demonstrate how option vanna causes the delta of an option to change with the IV which muddies the answer to “what did skew do today?”. Truthfully, this is a nerdsnipe for non-vol traders, but as a vol trader it’s bothersome enough that I wanted to choose a different tradeoff.
I opted for a standard-deviation relative surface for the study instead.
Let’s step through it.
1) Pull end-of-day GME data from 1/4/21 to 6/14/24
In particular:
.50 delta IV for the option closest to 30 day expiry (range of actual expiry dates in ranged from 27 to 32 DTE)
The breakpoints that correspond to 1 and 2 standard deviation OTM upside strikes estimated using .50 delta IV and actual DTE.
Call premiums at the closest strike to the breakpoint subject to some error tolerance (ie the strike needs to be within 10% of the breakpoint IV but that 10% is scaled to IV. If IV is only 30% than a 10% divergence from strike to breakpoint is not acceptable but if IV is 250% than it’s ok). If no such strikes were listed the day is omitted.
The vega of each option. I also estimate the vega of the theoretical ATM call using the approximation.4*S√t
Call premiums are normalized by measuring them as a percentage of the stock price.
2) Chart the 1 and 2 std dev OTM call premiums as % of stock price.
The .50 delta IV is on the left-axis. We can see the recent spike relative to the early 2021 spike. We can also see how the 1 and 2 st dev OTM calls explode in value.
But we expect option prices to rip when vol explodes.
Skew is an attempt to say something about how the relative value between options of the same expiry change. So far there’s is no notion of skew.
That sounds like a job for tracking a vertical spread as percentage of the stock price.
3) Chart the 1 SD / 2 SD call spread.
Hmm…this feels unsatisfying. The call spread is also spiking with the call values. We’re not learning much from displaying the spread.
There’s a good reason for that.
These call spreads, like outright calls have positive vega. As vol increases, OTM call spreads increase in value.
Instead let’s look at the 1×2 ratio call spread.
4) Chart the 1 SD / 2 SD ratio call spread (2 further OTM calls vs a single 1 SD call)
Ahh, now we are seeing the value of the 1×2 decline on spikes in vol. In other words, a structure that is long 1 OTM option and short 2 further OTM options is losing value when vol roofs. It’s hard to say what’s driving this however.
As IV increases, OTM options gain vega. Not only do the options go up in value, but they become more sensitive to IV. This is vol convexity. Every uptick in IV increases the option value more than the prior uptick. Like your position is growing! This is the “gamma of vol” or vol convexity.
At an extremely high level of vol, all OTM options approach .50 delta. The vega of options of different strikes will converge.
Assuming you own the lower strike and short 2 further OTM strikes, the 1×2 starts as a long vega trade from low levels of volatility. But it is short vol convexity or “gamma of vol”. At crazy high vols, the vegas converge and your net greeks converge to the net amount of options in your position — in this case you are net short 1 option. Your position vega, or sensitivity to IV, is now negative. So as vol spikes, the 1×2 loses value.
(Another way to think of this is that a 1×2 is equivalent to being long 1 call spread plus being short an extra option. At high enough vols the call spread’s net vega is a wash and you are just short an option.)
The picture above makes it hard to disentangle skew changes (ie the relationship between the 1 and 2 SD strikes). It is confounded by the changing vega of the structure.
Let’s back up and simplify for a moment.
We can compare the ATM call with the 1 SD OTM call so we aren’t trying to parse skew changes across 2 OTM options. And we’re going to control for vega itself!
5)The vega-neutral call spread
Instead of fixing a ratio such a 1×2. we will stipulate that our call spread must be vega-neutral. To do that we simply solve for the ratio that makes the vega of structure zero. In other words, we count how many OTM calls we need to short, for each ATM we are long.
The fewer options we need to short, the steeper the skew must be! In an infinite vol situation, all calls go to their maximum value — the stock price itself. Which means the call spread is worth zero (since all the calls are the same price) and each call has the same vega (which is weirdly zero — at infinite vol, changing vol by one point isn’t going to change the option value).
I like using extremes because they establish arbitrage endpoints from which to reason backwards from. In a high but not infinite vol situation, the ATM and OTM calls will not be equal. But perhaps the ATM call vega is just a bit higher than the OTM call. In that world, you only have to sell slightly more than 1 OTM call to be vega-neutral.
Repeating — the lower the ratio of the vega-neutral spread, the steeper the skew.
Here’s the chart.
Remember, this is a vega-neutral ATM/ 1 SD call spread. In the recent spike, the OTM calls were so jacked compared to the ATM that selling 11 calls for every 10 you bought would have been vega-neutral!
Let’s reproduce the chart but shifting the strikes to 1 SD vs 2 SD.
The picture is similar but the ratio to make the spread vega-neutral is more volatile. (That 2 sd call is also noisier because when the premium is only say 1% of the stock price, slightly leaned or errant marks matter more.)
Extra: A 1×2 indicator
By tracking the ratio of further OTM options needed to make a spread vega-neutral is an alternative way to track skew. Like normalized skew it reduces vol artifacts but because it maps to option premium as a percent of the stock price it feels more interpretable. “Wow, the skew is so high I can sell 50% less options to finance the same long premium” or “I can own 3 OTM calls for the price of 1 ATM”
In practice, the option markets tend to coalesce around some common structures. The 1×2 vertical spread is an easy to ratio to keep in mind. It becomes like a tool in the trader quiver…they might look at a surface with low or high skew and gravitate to “how’s the 1×2?”
If we fix the ratio as 1×2, accepting how its shorthand does conflate vol and skew effects a bit, we can create an indicator that has the same shape but lives on an oscillator — it’s bounded by 0 and 1.
To do that think of the extremes.
a) The most a 1×2 ratio call spread can be worth (from the perspective of owning the 1 and shorting a ratio of the further OTM) is the premium of the 1.
Example:
A stock is $50 and the 1 sd strike is $55 and the 2 sd strike is $59. If the 55 call is worth something and the 59 call is worthless, then the ratio is simply the value of the 55 call.
b) The least a 1×2 ratio call spread can be worth is the -(the premium of the 1)
Example:
Vol is outrageously high. There is little difference in premium between OTM strikes. In other words, the call spreads are worth very little. Much like GME recently where the 55 and 60 strikes were almost the same value. We’ll be dramatic and say both calls are worth $1. The 1×2 is worth -$1. If you buy the 55 call and sell 2 60 calls, you’ll collect a $1 credit. The credit cannot be larger than this since the 55 call cannot be worth less than the 60 call.
With an upper and lower bound on the value of the ratio we can simply compute the value of the 1×2 in relationship to its range.
Here’s a time series of the GME 1×2 oscillator:
Wrapping up
The point of this post was to provide more angles to rotate the idea of skew in your head. In the process, I hope I was able to convey how implied volatility influences option prices both absolutely and relatively.
As GME goes, the skew does in fact look like it climbed higher than it did in 2021. It’s most noticeable in the simple ATM/ 1 SD vega-neutral spread.
But the peak of the skew, wasn’t that much higher than the peak in 2021 suggesting the market adapted pretty quickly the first time around. After all, option market makers presumably learned “total nonsense is possible”. They had the benefit of the 2021 experience to draw from in setting curves and didn’t push it them too much further than they did back then.
The craziest event is always in the future, but it’s not unreasonable to reference the GME case as a point of comparison the next time skew explodes in a name and you are wondering “how ridiculous is this situation compared to the Roaring Kitty meme sheets?”
Food for thought
About 20 years ago, as a still junior option trader, I interviewed for an options trading role at a fund chaired by Myron Scholes. They were called Platinum Grove iirc. LTCM lineage. I wasn’t smart enough to work there. A fortuitous miss because I think they got blown out in 2008. I don’t know for sure so don’t quote me. (I can speak more freely in the paid letters but I don’t want to offend or misrepresent unfairly either. This is just what I remember and I didn’t care enough to verify.)
Anyway, one of the pre-screen questions was how can you construct a market-neutral long vol convexity position?
The answer they were looking for was a ratio iron fly. Assuming a “typical” vol surface, you can buy about 1.4 25d strangles for each ATM straddle you sell. The position will be flat vega but:
a) as IV falls you get shorter vol
Think of the extreme where IV falls to something like 5%. The strangle you own is worthless and you are short a straddle. Your vega is short. As IV falls, your vega falls. You are long “vol gamma”.
b) as IV increases you get longer vol
The straddle goes up in price but it doesn’t gain vega. ATM (technically ATF) straddles are already at maximum vega! But the strangles you are long, gain vega so as vol increases they start gaining value at a faster pace than the short straddles hurt you.
A ratio iron fly is equivalent to a ratio call spread + a ratio put spread. If you widen the strikes from 25d to say 10 delta maybe it’s a 1×2 call spread + 1×2 put spread. By tracking the prices of specific structures normalized to the stock price you can get a sense for how the vol surface is behaving without knowing the IV on the strikes themselves.
You will still some concept of vol to measure the distance of strikes from one another whether it’s delta or standard deviation.
You can also fix the price of structures and invert the questions — “how far apart are the strikes I need to construct a zero-cost collar” or “how far apart are the strikes that make the 1×3 costless”? Then the distances become values you can track in your analytics.
The more you can apply a familiar lens to various opportunities the more you can build a mental pattern-matching library for what looks “off”.
It might sound salesy but this very much why the moontower.ai approach is so dear to me. Once I left the desk, I felt blind because I was so accustomed to seeing markets from a lens that efficiently filtered what’s normal from abnormal amidst all the noise. As a discretionary trader, it was the ladder to the diving board. There were still steps to take before you jumped but most of the effort was handled in the canned measures.
moontower.ai is building to recover my sight. In the process, we can give other option users the same vision regardless of what their objectives are.
I caught David Boole’s segment about GME on CNBC because it was on Twitter. David used to cover me back when I showered every day. I agree with all of the framing.
He mentioned that the call skew in GME was higher this time around then back in early 2021. This made me want to look up the data but also prompted me to measure skew differently. But the “how to measure implied skew” question was a ball bouncing in my head already.
After publishing Scatterplot Gallery, Dave (not David Boole but an options market-maker) responded:
Dave is right. Sell side research likes normalized skew as a measure. So do I. We use it in moontower.ai. It’s how I looked at skew during my days at the fund and it’s the parameter I used at the spline points for my vol surfaces. I built up an intuition for those ratios over time per name. It’s also easy to compute.
Normalized skew is simple ratio of the volatility at an out-of-the-money point on the curve to the at-the-money volatility. It is common to measure at skew at the 25 and 10 delta strikes both on the upside and downside of the volatility surface and use the 50 delta option to normalize. (note the 50d strike is often but not always the at-the-money strike).
The 25d put is trading at a 14% premium to the ATM volatility.
But…
Dave is CORRECT.
The measure doesn’t really make sense. It’s useful because it normalizes skew to ATM vol, but the measure often has a non-linear relationship itself to the vol. OTM options are sticky at the extremes of vol — so normalized skew flattens when vol gets high and steepens when it gets very low. So if you wanted to know if skew is “high” or “low” you still might want to condition it on vol level. Which of course, negates some of the benefit of normalizing it in the first place.
In general, it’s safe to use because it will correlate strongly with alternative measures of skew — it still captures “high” or “low”.
But unless you are a vol trader accustomed to how that parameter maps to prices because you see it in a model every day next to option premiums, it’s abstract.
Measuring surface and skew changes is a big topic in setting vol surfaces (or sheets if you’re “book a colonoscopy years old”).
Today, we’ll discuss skew models which will serve as background for next week’s paid post where we:
look at another measure of skew in the spirit of Dave’s comment
apply it to GME and David Boole’s comment
For both posts, we will be visual and lean towards simple.
Skew Models
Skew models allow traders to parameterize a vol surface. In other words, fit an IV curve to a discrete chain of strikes. From cubic splines to the vanna-vega-volga model, you can gorge yourself on as much complexity as you want.
Us knuckle-draggers who think an ecole is something you get from bad burger meat are just going to throw a line through some points. This is an example from the famous TT software:
The vol curve requires:
ATM or ATF VOLATILITY
Implying an ATM vol from the market or setting your own:
BREAKPOINTS
Finding the IV of the strike at various moneyness, SD’s(standard deviation points) or deltas. Any of these measures is an attempt to measure the distance from the ATM strike to the “breakpoint” (ie 25 delta or 1 SD). Careful, moneyness is not a normalized measure. If a strike is 5% OTM, it’s much further away in a 10% vol name than a 50% vol name.
Example
The pictured model has 3 SD points above the ATM strike and below the ATM strike. Beyond 3 SD’s there will typically be a linear slope coefficient that fits the tails. That IV can then be parameterized by its ratio or spread to the ATM vol. So if the 25d put is 33% and the ATM put is 30% we are running a 25d put skew of 3 vol points or a ratio of 110%. As we’ll see, there’s no right way, just trade-offs.
Comments
The goal is fit the market snugly but without creating arbitrages in the option premiums due to weird kinks. These curves interpolate vols for the strikes in between the breakpoints. Market makers play whack-a-mole with kinks that get out of line.
Deal stocks or other assets with idiosyncratic behavior around specific price levels (think of how coal-switching puts a floor on nat gas prices) usually don’t have bell-shaped distributions. It’s hard to fit curves to them. Wrong tool for the job. That’s what Excel and some common sense is for.
As mentioned earlier moontower.ai uses normalized skew by delta
On modeling skew changes
“Sticky strike” refers to a model that assumes strike vols (vols at specific dollar strikes) stay fixed. This is reasonable over short horizons or smaller moves. It’s unlikely to hold over the time frame in which an OTM 30 strike put becomes far ITM
“Sticky delta” means we expect IVs at various deltas to maintain a stable relationship with the ATM volatility. This is an implicit assumption if you use normalized skew — “I see that the 25d put seems to persistently trade at 110 to 115% of ATM vol”
There are hybrids and permutations. In a professional setting, that gamut ranges from highly bespoke proprietary models to a wide array of vendor software. I’ve used many types of models. Spot-vol correlation parameters were much more widely used in my second decade of trading. I’ve even used flat sheets, no skew at all. I’d just have a mental log of how far from flat sheets options of a particular distance from ATM would trade. I’ve used models that don’t have vols — everything is handled in price space. The models themselves were never a source of edge. But if a scale is consistently adding 2 pounds it’s still useful for comparison as long as you weigh everything with that scale.
This is why normalized skew is fine for cross-sectional comparison. It answers the question you’re interested in even if it’s hard to interpret on its own. The truth is measuring skew is like trying to pinpoint a firefly from its sporadic bursts of light.
Consider a made-up $20 stock with a 6-month IV of 40%. I fit a dumb skew model to it (it’s an Easter egg for a certain group of people, all of whom likely have reading glasses by now).
2) Let’s look at the $24.50 strike. We can describe that strike in many ways:
22.5% OTM (moneyness breakpoint)
.25 delta (delta relative breakpoint)
.72 SD’s OTM (standard deviation breakpoint)
3) We can describe its skew:
3.9% clicks below ATM vol (spread relative)
9.8% discount to ATM vol (ratio relative aka normalized skew)
Like good little option taxonomists we can say lots of little things about our friend the $24.50 strike.
But now we shall kill him.
Some hedge fund wiseguy with an S&M fetish puts on a giant collar — buys puts and sells calls. Ravages the skew.
The ATM vol stays the same, the collar is vega-neutral. But we’ll assume the 24.50 call’s fixed strike vol drops from 36.1% to 32.3%, nearly 4 full clicks.
What can we say about this option?
Well, it’s still 22.5% OTM.
It’s still .72 standard deviations away since the ATM vol hasn’t changed (assume it happened quickly, so not much time elapsed).
The normalized skew has changed. The strike now trades at a 19.3% discount to the ATM vol (32.3/40 – 1).
That’s important. It tells us our measure is working — the call got hammered relative to the ATM and the discount got wider. Basic counting still works.
But we have a small problem.
If we parameterize our surface by delta we have a “nail Jell-O to the wall problem”. By virtue of the vol coming in, the delta at the strike also falls (this is also known as “vanna” — the Commander-in-Chief of greeks — getting both too much credit, blame, and airtime relative to its efforts).
The $24 strike is now the .25 delta call. Its vol is 32.9%. If you are looking at skew changes using delta relative parameterization you will see skew fall from -9.8% to -17.8%. A steep drop but not quite the drop to -19.3% change if you used standard deviation relative or fixed strike relative breakpoints.
Summary:
Pictures are always better for these things:
The nuances of tracking skew changes are to finance what Equus Erotica is to sex. Like 40 people care.
Other sources
I’m not at liberty to blast it out but this was a widely-read piece on measuring skew:
You can also see Colin Bennett’s free book. My notes are here.
Just remember…
The delta relative breakpoints are recursive in that the strike vols changing alters the strike deltas.
SD relative breakpoints slide around with the ATM vol and time passing.
Moneyness breakpoints jump around with every tick in the stock.
Whatever you pick, just be consistent and understand its biases. And when I say “you” I mean pros. If you are anyone else losing sleep over this, you’ve lost the script.
Options stuff is fun, “bicycle-for-the-mind” and all that. Just don’t think you need to know this. There’s no money printer at the end of this rainbow. It’s mostly useful for managing the risk of large option portfolios — the less stuff you trade the more irrelevant this stuff is.
You’ll go far in life if you can just be good enough to remember your hole cards and not need to check’em again to see if 3-7 offsuit is playable.
I’ve been narrating my small GME trade this week through this substack and twitter.
On Friday I rolled my short June 20 calls to the 25 strike. I narrated my thinking on twitter but I’ll re-print it here. It’s a combination of real-time thinking and some meta-thoughts about trading as well.
Sharing my monkey thoughts as i mess around in GME… I’m long that 20 lot of June 20/30 call.
Rolling the position
Despite the stock being down today, the 30s are eroding as vol is declining so the spread actually upticked in value.
I’m also looking at the june 20/25 call spread:
From my IB montage
The spread value has increased a lot. The vega on these options is small but not totally negligible. Look at the IV spread…it’s fallen 14 points today on a spread with a penny of vega – that’s a 14c rally in the spread on a delta deutral basis! Since the spread is only .23 delta, the vol change has kept the spread little changed despite the stock move.
I decided to roll my short 20s into short 25s.
So I sold the June 20/25 cs. I was filled at $3.71
I was long the June 20/30 cs from $2.08 but collected $3.71 on the 25/30 cs.
=> On balance, I’m left long the 25/30 cs for a $1.63 credit.
Thinking behind the roll
The roll was driven by a sense that the risk-reward on the 20/25 cs at $3.71 is not as great as owning the 25/30 for a m-t-m level of $1.60.
I’m synthetically “selling the 20/25/30 fly” in my reasoning.
This is a mix of seeing the strike vol changes today and feel. This may sound woo woo. If you require higher standards of trade discretion I can understand that but for the most part this is kinda what trading looks like for all the nerdom that gets bandied about.
GME is a name that doesn’t lend itself to data analysis or cross-sectional triangulation.
[Also, these are microscopic stakes —the original trade only risked about $4,200 and was only 1/5 of the size I wanted to scale into. Unfortunately, the call spread went straight up in value after I was filled and I was too anchored to chase]
In a professional setting, you will be more plugged into flow which tightens the reasoning and timing plus better execution tools/costs, but the mental progressions of a MM very much rhyme with mine especially in idio situations.
The value of tracking
After selling the 25/30 call spread, I stored it in my watchlist on a delta-neutral basis vs the stock price reference I sold it against to track its performance and my fill quality.
The market on a delta-neutral basis is $3.52-$3.89, I sold at $3.71.
June 20/25 call spread
I noticed as the stock went down my fill marked better and vice versa.
This can be an artifact of market widths in the legs esp since both calls are ITM but if you can rule that out by tracking the counterpart put spread instead (CS + PS = Box so you can translate the 3.71 cs as a 1.29 PS) you can get a fingertip feel for how the skew moves as the stock changes by watching a delta neutral price move. I used to do this for lots of structures. They’d be in my window for weeks so I can see how certain large trades worked or not.
Experience is a repo of unstructured data
Overall, these little habits accumulate as a big unstructured data repo otherwise known as experience. Discretionary trading uses “science” for measuring. models, dashboards, stat studies. But the trading is a boardgame sitting on top of that.
Systematizing
Systematic trading is different. I sat next to people running large systematic strategies. It’s piloting & auto-piloting a more diversified strategy, less chunky risk but it’s not an alien approach. It’s also inspirational because you can port measures and ideas from it
I never really figured out how to systematize my trading from end to end. I like to say discretionary trading is just trading without ignoring unstructured data. The unavoidable pitfall is part of that “unstructured data” is bias however.
You can fight that with a team of people conscious of behavioral biases because while it’s hard to debug yourself it’s easy to call out others’ blindspots. You can help each other. (see Trading Is A Team Sport)
moontower.ai
It’s funny as I’m sandboxing analytics to develop for moontower.ai, I’m always thinking about how to pre-chew ideas for users.
There’s always a balance between legibility and user effort. If investors just hand you money to manage for them, it requires no effort for them but they have no control over the trades or process.
At the other extreme, you can give a user a Bloomberg terminal where they have full control but need to make all the decisions.
For a retail user this trade-off requires tremendous thought. You could just feed someone a signal without teaching them how to fish. When the signals don’t work they’ll churn. Or you can teach them how to approach their goals methodically understanding that there’s a learning curve. It takes more effort for the user but for the person who wants to learn to fish it’s the only way.
moontower.ai balances being opinionated but not signal-driven because it inherits the exact trade prospecting funnels I used as a discretionary PM.
We can see the seeds of signals in our “axe list” concept. It’s just a roadmap idea at this point. But some of the data play I’m doing for this coming week’s paid post looks like it might be a source for another analytic regarding skew.
As a reminder, if you’d like to signup for moontower.ai as a paid user, a moontower.substack paid sub is included.
We also have a fully automated affiliate program. If your audience would be interested in option analytics with a point of view…you can sign up to be an affiliate and get $100 for users who sign up.
A Twitter friend thought he might have found an arb in the ADBE options that could be exploited by a trade known as a ‘conversion’. It was a false alarm but if you scroll through the thread you can learn a lot about computing implied rates and the details of how to execute the conversion arbitrages. They don’t sit around in plain sight but this is the masochism section so if you want to learn the thread is a real-life process of noticing something that looks off, getting to the bottom of it, and learning a lot about options in the process.
The lingua franca of asset management regardless of strategy is returns. But this is not necessarily true in trading. In my own 21 years of trading, it was never even brought up internally. It gets mentioned somewhere far in the background. In vague terms at best. And even then, the context is more of a hurdle than a target.
We’re going to talk about this in 2 parts.
Today
I’ll walk through what this meant in the 3 phases of my career (with plenty of color interspersed):
Being a market maker at SIG
Running my own market-making group financed by a Chicago firm that backs traders
As portfolio manager within a relative value volatility trading hedge fund. This last job was for an entity that was backed by LP money and therefore beholden to the concept, language, and delivery of returns. And yet, the idea of returns was alien to how I ran my business there.
Next week
I’ll connect this back to a reader question that got me thinking about all this in the first place:
How important is (il)liquidity in options when making risk-defined trades such as credit/debit spreads or buying single call/put options?
Hmm.
I can feel the doubt.
“Bruh, those lily pads are in different ponds, how we makin this leap?”
We gonna make it. Off we go…
At SIG
My first trading job for SIG where I had my own account and P/L was an equity options market maker on the AMEX floor.
The AMEX, like the NYSE, is a specialist system. There are “posts” where the options on a list of tickers trade. The specialist is like a lead market-maker who sees the full order book and is required to make a market according to a set of rules and guidelines. The specialist designation is a bundle of obligations and privileges. They must maintain an “orderly” market, set the vol curves which then disseminate electronic bids and offers for every strike and maturity for a name to the world. They are also entitled to 40% of the volume that trades on the bid or at the ask.
Market makers stand in front of the specialist post and announce any bids or offers that improve the specialists’ market. The market-makers are allowed to participate alongside the specialist on the bids and offers if they agree that they are “on the market”. My first year trading, I was a market-maker. The major names at my post were AIG, Qwest, Eastman Kodak, Corning, Cheesecake Factory, and about 25 other stocks. One that was notably missing because it was just delisted from that post — Enron.
As a novice trader, it was really about strapping on a helmet and getting experience. I wasn’t going to be taking massive risks but in the course of trading if I saw anything noteworthy I could discuss it with my manager to see if I should be. There were 3 notable things that happened in my time there.
AIG accounting scandal (this was the only time I ever talked to Jeff Yass about a trade. UBS put up a giant print in the options and Jeff dm’d me to call him with details on one of the black phones placed near the trading posts. I was scared shitless to call because I didn’t do any part of the trade and was afraid he was going to undress me for missing it. He just listened, thanked me, and hung up. I never heard another word about it).
Massive buyers of Qwest teeny puts by cap structure arb flow who were trading puts vs CDS. Selling them week after week in size and overhedging the hell out of them made my year. It was also stressful because up days were painful, but the stock leaked lower and the puts barely budged.
[A year or two a colleague ran the same playbook in Xerox in much larger size and had an amazing year. If I remember correctly, that fellow was banned from Vegas casinos for card-counting by the time he was 22. He left SIG after that year, 25 or 26 years old, co-founded a prop firm and retired very wealthy in his 30s. Our wily friend also made the news for a buying a call option on a penthouse from its owner that ended up being the highest value residential RE trade in the city where it happened. Not a small city. One funny thing I remember about people’s impression of him — he was very lazy but insanely smart. And despite my personal belief that endurance and effort > brains, there were a lot of counterexamples to this back in those days. There were savants who struck it rich and peeled off. The billionaires in the options world were the savants who worked their asses off to build businesses, but the clever cats won life. You got $50mm in 2009 and your like 33 years old. You’re gonna triple it by age 50. In flip-flops with a flip phone.]
I found a dividend in Kodak that was being priced in the wrong month. Which brings you to the question — how do you pick off the people who stand next to you all day with a structure that doesn’t tip them off too quickly and also disguises that it’s you?
[This is a separate topic but trading cultures revere cleverness. It’s a game where the goal is to take people’s money. Any harmony is just a long-run game theoretic compromise. It is fundamentally adversarial. Can you see why effective altruism starts to look like effective autism when you consider the frames traders must adopt to deal with the discomfort of their decisions? At least back then the sociopaths were more forthcoming in their intentions rather than torturing normal people with trolley problems.]
After a year at that post, I was moved to one that included Microsoft (I was there when they announced their first dividend — it was special $3 div I believe), Oracle, and Expedia. That was 2003. After 2017, 2003 was my second least favorite year. There was less action compared to prior years and markets were getting tighter (the purely electronic ISE grabbed a ton of market share). I felt deeply discouraged. I came into the business near a peak and this was my first downcycle. I extrapolated doom.
So what were my returns in those first 2 years?
I have no idea. I had a close to $1mm profits in the first year and broke even in the second year.
I don’t know how much capital I used. In fact, they wouldn’t want me to know. For example, the margin I was paying financing charges on is likely much higher than it what it was in reality considering the difference in rates a small trader gets versus a giant client like SIG. It would only make sense for the partners to effectively lend me the difference rather than allowing me the credit for funding at the firm’s rates. It’s 6 in one hand, half dozen in the other when you zoom out but it does obscure your true rate of return. It wasn’t clear how much margin you are using or how much it varied. And they had no incentive to elucidate this.
If you were looking to leave then I’m sure you could have backed into a good guess for how much capital you needed. Which is critical if you are looking to build one of these businesses since of course it’s still a capital allocation decision whose ROI must be compared to other uses for the cash. But when you are making the donuts, there’s no talk of return.
So how do you talk about the business?
It’s raw dollars. Management figures “Ok, the average MSFT market maker for SIG should trade 5,000 lots a day for a penny of edge (remember the multiplier is 100, so it’s a true $1 per lot) times 252 trading days — the spot is worth $1.25mm per year”.
[If you make less, they’ll ding you in your bonus, if you make more, they say the trading was better that year so you were expected to make more — here’s your expected bonus. If you get discretionary bonuses you know the routine. You’ll get a verbal reach around in your bonus meeting, but then the number falls short of the rhetoric. I’ve been able to laugh about this for a long time now, but my wife can remember the days where my traders friends and I would plan what we would yell as we “flipped the desk over” 3 months in advance of our disappointing meetings. No matter how much you get paid, it’s always a letdown. She would joke about the Trader Wives Club where they’d have to hear us whine for 3 months before our reviews, and another week afterwards.]
In short, a trading spot occupied by a someone who knows what they’re doing has an expected p/l with a distribution. Based on the activity in the names that year, the value of the spot could be upgraded or downgraded for the following year. There’s always a dollar target and and the outcome is a debate about how much skill the trader brought to the result versus how the assumptions of volume, volatility, and competitive forces varied from the start-of-year forecast.
If the cost to man the spot makes sense compared to the expected p/l, someone will be assigned to it. Spots that are more valuable will be staffed with the more experienced/talented traders (ie you should expect that meme stocks are piloted by a prop firms’ top traders). So while there’s no concept of return, hurdles and opportunity costs are baked into the staffing decisions.
Backed by Prime
From 2008 until early 2012 I was backed by Prime International, a prop firm based in Chicago. Back then, they bankrolled about 100 traders, many in futures but there was several option pods of various sizes. I ran a mid-sized one and shared an office with their largest one (that pod was the largest market-maker in crude oil options in the late aughts).
These years were the most fun and learning I had in my career, outside the first year out of college as a trainee which was a zero-to-one combustion. I’ll save the stories for a non-print medium. I vaguely remember colleagues researching what it would take to create a small ice rink and get a penguin for the office. The fact that I would have put a 25 delta on it actually happening is a pretty good indication that this was not a normal work environment. Any job after this was gonna be a letdown but the floors’ days were numbered.
With the backer, everything was transparent. I was getting 70% of my p/l. I could see my daily margin. My shared and non-shared expenses. I could hire and fire as I wanted.
Yet again, no concept of return.
If you just looked at margin, you could back into an expectation that you should return 50-300% per year to make the gig worthwhile.
[This was in fact typical but I don’t think any pod back then was using more than $10mm and most utilizing less than $2mm. Floor trading isn’t that scalable. Ironically, the way to keep a floor well-fed is for fiduciaries to trade as if markets are more scalable than they actually are.]
Unfortunately margin isn’t a great denominator for returns. Buy a bunch of teeny options and you can mask risk. You could hunt for the cheapest thing to buy that makes a concern, defined too objectively on the back of assumptions, go away if you know what canned scenarios the risk group runs. I’m not saying this is done on a conscious or nefarious level but it’s too easy to affect the Ouija board by having a little extra preference for this strike or that maturity.
Computing return on average margin can also be weak depending on the nature of a strategy. Margin calculations are coarse proxies for risk. They aren’t custom enough for option traders. At one end they can be gamed, and on the other end they can be too conservative for arbitrage strategies (for example, no margin relief for WTI look-alike swaps if one leg is on ICE and the other on CME).
A picture is emerging. Return is difficult to compute because the denominator is murky.
We are accustomed to returns and volatilities. They let us use Sharpe ratios to measure risk-adjusted performance. But if we don’t have returns how do we get to risk limits that make sense? How do decide where to put capital?
Hedge fund days
In 2012, I moved to SF to build the commodity relative value volatility business for Parallax. It is a master fund with a host of sub strategies. LPs see returns but internally there’s no concept of returns at the strategy level. It’s just p/l that rolls up to the fund level. To be clear, this is typical for such a structure. It’s flexible.
The fund posts margin and manages risk such that the margin to equity ratio stays comfortably under 100% even in stressed conditions. Which means there’s always a cash buffer which can be held in T-bills, box spreads, or managed in any highly liquid way.
The sub-strategies margin requirements will bounce around based on the volatility and opportunities in the markets. Just to make up numbers, imagine the firm aum is $1B and runs 50% margin-to-equity. So in typical conditions, the margin requirement is $500mm.
Now consider that my margin requirement in the commodity book ranges between $20mm and $100mm depending on how much risk I’m taking. If I was a standalone fund and to be highly confident that my margin-to-equity wouldn’t exceed 80% than I’d need to raise $125mm. Most of the time I need much less, which causes a drag on returns but in the master fund structure I don’t really worry about this. The firm’s excess cash isn’t allocated to strategy as a hard constraint. The GP acts as the ultimate capital allocator internally.
So the best guess of what my returns are depend on the flawed denominator of average margin and relative to that number, they will always be worse if I’m a stand-alone fund because I need to raise far more capital than I’d typically be deploying.
How did it the business work in practice?
You’d come up with an annual expected p/l. In my case, the median was about 70% of the expectancy because I ran a positively skewed book.
[I was typically long vol convexity and often long gamma. When I was at Prime with my own money on the line, it was not uncommon to be paying 4 figure theta bills. I stood next to a guy that traded 100% of his own money that had a seven figure bill a few times a year. (Random thought but learned a lot about playing the player not the cards from him but this was a small market which he would turn into a game of heads-up no limit with the big customer. He recognized he had a lot of edge, and pushed. I hope he shifted gears when that was no longer the way you could play.)
In my fund book, you could buy a Porsche or Lambo every day with with the theta. That said — I kept a close eye on a very simple measure — don’t be long too much extrinsic premium unless there was a specific reason.
VRP language is something that feels like it comes from the asset management world not the floor trader world. There are exceptions. I knew some large short vol traders at every stop. The biggest lesson is that this game is far more artful than risk premia discourse pretends.
As for my own long vol bias and performance — this was not some trick of “Oh I lost half my years but won more in good years”. No backer, prop firm, or absolute return fund would tolerate that. I broke even or was down small 3 out of 20 years, made medium amounts most years and put up the numbers that drive the mean from the median around the GFC and the 3 year period spanning from the 2018 Volmageddon (although I wasn’t directly involved in that trade, it was the return of vol after the 2017 idiocy) through 2020. Look, the job pays when people are in pain. I don’t know what to tell you. The rest of the time I watch beta-maxxers and PE suits buy mansions. I write to feel prosocial. I don’t need trading to that feel that way. Sensing a dumb counterparty squirm, one who almost certainly was getting paid too much previously for charlatanism, is a reassuring hug from the god of markets as far as I’m concerned.
I am an agreeable human (I’m like 95th percentile on the Big Five personality test for this) but a highly disagreeable trader. Process, patience, fold, more patience, then f you sold. Boring, boring, boring, paper cuts, I hate this job, boring — violence. Put your style into simple words one day. It helps steer you back to the North Star whose light whose light you’ll most when your every decision feels like it takes you further into the dark.]
Back to the returns stuff. You peg an annual p/l target. Management implicitly considers how much risk needs to be tolerated to achieve that raw p/l, deems it satisfactory and off you go. Next year, the landscape is reviewed, growth initiatives weighed and you repeat a somewhat informal process. Any course-correction is mostly handled ad-hoc as the PM sees whether or not the environment calls for taking more or less risk. You can tell when there’s too many predators (entities who see the world in a similar way to us) vs prey (customers that have hedging or punting desires). There’s a time to hunt and time to hibernate. I say it all the time — this is a biological system not a Newtonian one.
So back to returns…it’s not quite right to think of return on margin. If you want to force a business like this into that framework you should probably just be conservative and consider how much AUM you’d need to run the strategy as a stand-alone fund. I’ll use a broad informed stroke. With a few hundred million in capital, I’d guess a strong manager with a trader mindset (as opposed to asset-manager mindset — if you’re in this business you know the difference so don’t @ me) could put up mean returns in the ballpark of 9-12% with the median between 50 and 70% of that.
[You can also see why many of these business are best housed within a fund that can flexibly allocate unutilized cash. The traders can be paid well enough to not tempt themselves into the brain damage of starting a fund of their own. To go out on your own has to be about more than money. There needs to a psychic reason to want your name on the door to endure what it takes to launch a fund.]
This is a damn good proposition because it behaves like long option position that you get paid to own. It’s unsurprising that the fees for the handful of managers who can do this (if you can even access them) are high. The proposition gets much worse if you’re taxable because it’s a short-term gain bonanza but of course many institutional allocators are tax-exempt.
Most of the risk lies in the ability for talented group of people to self-perpetuate themselves and the ability to assess that from the outside is probably almost zero. So all the usual caveats of active management apply.
Like I said earlier, next week I’ll tie this back to a seemingly unrelated question:
How important is (il)liquidity in options when making risk-defined trades such as credit/debit spreads or buying single call/put options?
Gather round. Let’s just chop it up in no particular order.
On Monday, I fired off an impromptu email with a trade I was doing. Disclaiming of course that it’s not a recommendation. I have no licenses and I’m not qualified to give financial advice. Buyer beware and all that. I sent it to paid subs only.
Actually, let me clarify the paywall. Last year I added some paid tiers on Substack. It was like $150/yr. There was also a $500 annual OG tier. For $150, it was just a chance to support the letter and OGs had that satisfaction plus a Zoom or IRL chat if they wanted. In other words, there was no extra content for paying. It was just a tip jar. I support other writers even if the content is free so I understand the impulse. Who am I to deny givers. So put the tiers in.
I have a friend in my book club who is a marketing ninja (people throw such superlatives around but this mf’er charges really high rates for good reason). He offered to “look at what I’m doing on the internet” pro bono. He saw how many people were supporting Moontower at the regular and especially OG level and remarked it was quite unusual for those percentages considering they weren’t getting any extra content. Paraphrasing: “Kris, people want to pay you. You just don’t give them an excuse. For many people it’s hard to pay for something even if they want to because the official price is zero. It’s a psychology thing.” Reminded me a bit of the “penny problem”.
I explained to him that I actually felt guilty or a sense of reciprocity for not delivering anything extra. But I feel strongly about giving away a lot for free. Charging also felt off.
Taking a longer, realistic view — time is time, and I give this letter a lot of time. I’m not some alien for whom this comes easy for. So the eggshell that idealism always rests in has cracks in the form of opportunity cost. The compromise to satisfy both my guilt and test his thesis that more people wanted to pay was to paywall a small fraction of my writing.
Anyway, that’s the genesis of the paywall. I’m happy with the mix. I feel better about all the guilts — opportunity cost of time, giving extra to payers, and not withholding what I hope is value for people who won’t or can’t pay.
The paywall also seemed like the right venue for sharing a trade I was doing. It’s a bit safer space since I don’t think anyone pays to hate-follow.
I’ll add— if you converted to paying because you think I discuss trades all-the-time you’ll be disappointed. I suspect I might do it more especially as my personal trading infra gets better with moontower.ai but I’d rather underpromise on the writing and let this place be a source of pleasant surprise instead of having it start from a transactional place where I feel the invisible pressure of coming up with stuff for the sake of delivering something that sounds useful. If I tell you I like something it’s because I do it. And it might be dumb. But that’s why it’s never a recommendation. You can only count on me translating what the turd-throwing monkey in my brain says back to you. You decide if that’s worth paying for, either way I’m publishing plenty of free stuff and some not free.
Moving on.
I did in fact do a trade. If you follow me on Twitter, I’m transparent and I even shared screenshots. I’m more Whimpering Puppy than Roaring Kitty but my real-time thought narration is less cryptic than memes. SO, I have that going for me.
I bought the GME June 20/30 call spread unhedged. I only bought 20. My intention was to buy 100. I was comfortable risking about $25k. I got filled at $2.08 giving me almost 4-1 if the stock expires $30 or higher. Unfortunately I left a bunch of dead soldiers (unfilled orders) behind and the stock got up to $30 the same day. $4k turned into $8k and I’m just mad. As Agustin Lebron preaches in Laws of Trading — “you are never happy with the size you trade”. It’s always too much too little in hindsight.
Although I didn’t share the trade idea in the free substack, I did share lots of thoughts publicly:
Messing around a bit. Used an option calculator and ran 300% flat vol sheets vs skewed vol sheets that roughly fit the market just to see how different the distributions are (stock ref $25 in $GME)
Which was a follow-up to:
Flat vol is what old people would call flat sheets. As if you ran the same vol on every strike. My gut market on this call spread if I’m allowed to be wide would have been $7.75-$8.75 knowing it was volatile squeeze stock with 2 weeks to expiry.
[This isn’t actually a short squeeze but it’s the only mental model I can match it to]
Looking at the table, my $7.75 bid would simply get tattoo’d. Anyway, hoping tomorrow the setup invites a little gamble. If we get more of the same flow as today, I’ll get the chance.
Back to the butterflies:
Fly density is just butterfly centered on the middle strike divided by the strike width. This is why vertical spreads are model free bets on the distribution. A lot of call skew or vol pushes the modal outcome to the left.
High call skew makes call spreads cheaper which implies lower probabilities of the stock going up. Which is why my original tweet is looking at how cheap the call spreads are and the market implying the stock lower.
Here’s one more this time including what a regular 30% stock distribution looks like to the picture (again using flat vols):
You are getting unusually high odds to bet the stock is not going down by June expiration.
This is the same idea I’ve pointed out in winter gas or H/J nat gas CSO’s. When call skew is nuclear or stocks short squeeze for options market bidding for upside actually implies the stock is probably going to drop (which is consensus in a squeeze…it’s just a matter of when and how fast).
The down moves are stabilizing. Think of the up move as potential energy of a stretched rubber band. No matter how far you pull it the expected snap back point is the same. In fact, the bigger the squeeze the more likely the capitulation happens because the last short says uncle and represents the last buyer. There’s nobody left to buy.
This is why when when assets squeeze the put spreads get expensive. Consensus is down not up. Up is destabilizing, higher vol territory. Remember how you want to own the options AWAY from where it expires.
This is a classic demonstration. The market wants the options in the direction of the skew. It wants the “it probably won’t get there but if it does things are gonna break, yee haw!” It doesn’t want the options of where the stock will land. Or inverting, where the options are cheap (the cheapest body of a fly, therefore the most expensive butterfly) is where the stock is implied to land.
This account had good questions. I gave my best answers.
One account rebutted that options don’t just sit overnight with positive EV sitting in them.
Hey, I mostly agree. But this is a coin flip I believe the odds compensate for. Nobody knows where it’s landing. If RK rolls or changes his position the odds change…the most egregious dislocations in the surface probably fair up and something else breaks. In the tree of possibilities, the trade can work simply by the turn card coming out (ie new information in the form of flow that shuffles the deck in a new way). I don’t need to take this into expiry. I think there’s edge in the levels.
Here’s the thing — nobody has some quant model that knows where this thing is landing. This is a pure trading situation. Of course, I can be wrong. Hell, I told my wife I’d guess I have a 50% chance of incinerating the premium which is much higher than what flat sheets or a lower vol name would suggest.
But I have several ways to win. If go to the grave with these, I do think I’m getting odds because the market had to absorb this flow by moving the spread. It can’t diversify it away. Another way to win or at least manage the position comes from trusting my judgement on how to think about the matrix. You do this long enough, you chunk an options board the way a chess player chunks familiar patterns. “Hmm, that fly looks too cheap compared to that one…ahh when I try to execute I find out it’s not really there”.
As trading goes, this is not the hard part. What’s hard is when things are grinding tick by tick. That’s a miserable nerd market that burns my eyes. I don’t have opinions on stuff where everyone can think all day and night about what something is worth. In fact I don’t have opinions often. Right back to the “options don’t just have positive EV sitting in them”.
I do think you can make better decisions in the options landscape but that not the same bar as being a pure alpha option trader. That last bar is really high. The market likes to give you false directions to that party. It’s important to know what circumstances your heuristics are more likely to apply. Trading requires the tacit knowledge of when to switch gears between “I need to act without full info but right now I can act with even less info because the amount of info anyone has is not as high as it usually is”.
One last bit.
The reason I even looked at GME closely was serendipity. A friend had an angle on GME he wanted to bounce off me. It was a pet idea. Kind of weird but also something I thought similarly about in the psychology (which I don’t think is a view most people managing money would come to). It’s not a 4D chess thing either which is something I’m generally skeptical of anyway.
But chatting yesterday, he made an off-hand comment that highlighted why options are so interesting.
He texted:
all the probabilities are skewed to make people get long lol
This is exactly, what the cheap call spreads do. Which is why we say “they imply the stock much lower”. Again look at those fly distribution pics. You only make that statement if you understand options. But here’s the rub…what is the counterforce? What’s the thing that makes people want to get short not long?
The stock price itself.
It says get short. If you have an investor’s horizon you think, why is anyone paying $9B for a couple billions worth of T-bills*? Meanwhile, the options offer odds to get long.
[*On Wednesday it came out that the at-the-money share offering raised $2B….hmm and all it took was a few days of the stock trading in the 20s to absorb it…sounds bullish to me.]
The question of fundamental value has zero relevance to the now. It’s like using a yardstick to take the temperature. Don’t mix up the dashboards you use for long-term ideas for the gauges you use to consider the short-term.
And finally, we couldn’t resist…
while we are about to double our ETF coverage on moontower.ai we just had to add GME.
Seriously, I’m stoked about how moontower.ai is coming along.
(If you use options, you should check it out. If you are just curious you can still sign up for free for the educational materials and MoontowerGPT)
A collateral benefit of the moontower.ai work is personally getting to spend more time in Jupyter notebooks as I sandbox ideas that are coming down the pipe. Coding is not a personal strength, I rely on Copilot A LOT. I only recently started using Git. But getting to build, learn, write, code, and bring together analytics in a way that leads to better decisions, practical actions, and teach is a super satisfying way to spend time. [By the way, nothing I code goes into production, that would be malpractice.]
These opportunities wouldn’t have come together if you didn’t give me a little hamster wheel in your brain to run on. I know if I do a good job on all fronts that elusive sweet spot of “sustainable because it’s valuable” and satisfying is possible.
It’s going to shock you to hear it, but I get emailed a lot of option questions. I’ve gotten some that are pages long with commentary, prices, blood type.
This is one of the reasons I put the shingle up for calls. I’m definitely not reading all that free, but also I can talk through options stuff way faster than I can read and write about it. You’ll say 500 words about what your doing and I’ll collapse it into floor trader grunts in the time it takes to pick up a handset and say “sold”.
I spent my whole adult life having to make option decisions in a few seconds. This is not anything special — talk with any market-maker and their fluency with calls and puts seems like a parlor trick. Options are just another language and being fluent in it means you think in that language natively. The old floor folk can even sign in options as fast as you can talk. (I can read the signing but I was the tail end of futures being traded in the pit and not on Globex. I never developed a large hand signal vocabulary).
That said, if a sub sends me a question that I can peck on my phone in a few minutes I’ll just answer it. (Also I read every email I get and try to respond to all of them even if it’s to acknowledge that both I and the sender are humans worthy of not being ignored.)
If responding to an email takes more than a few minutes I’ll pass it through the “would other people care about the answer to this question?” filter. If so, I can kill 2 birds with one stone. Oh my god, F me that’s a horrid idiom. The first person who ever said that should have been locked up on the spot cause that’s I-knew-he-was-a-serial-killer-when-he-was-nine level of clue. I never thought about the literal meaning of that expression until I typed it.
Re-phrasing — today is one of those moontowers where I can pick up the 7-10 split by sharing a response to a reader question that you might find useful.
Reader question:
Do you know of any way to model an option’s price intraday?
My response:
2 things I’d think about:
1. Intraday I would think in terms of straddle prices and price changes and compare that to tick vols (but the tick vols themselves can also be in price space not vol space)
2. Modelling the fraction of a day’s variance that typically accumulates every hour (for example the open represent more of the days volatility then any random 15 minute interval)
Reader reply:
When you say you would think in terms of straddle prices and price changes, how would that be used to model the price of a specific option? For example, if someone wanted to model the price of the 190 strike call 5/24 by the hour tomorrow relative to AAPL’s price, what should they do to get a rough idea?
I’d start with the question of:
“What do you think the straddle is worth every hour?”
So if half the day is gone, the straddle is worth: 1% * sqrt(.5) = .71%
The question is at what time do you think only 1/2 the day’s volatility remains?
This question applies to every hour of the day.
The entire concept of “intraday decay curves” is area of active inquiry for any market-maker so I don’t have an answer key but the problem is familiar.
In practice, I’ve tackled this with a blend of lazy guessing and leaning on some quant research.
The lazy way
The 80/20 solution or guess would be to assume volatility transpires at the same rate volume unfolds over the course of the day.
I prompted perplexity.ai with “vwap volume distribution over the day”. To my delight it didn’t send me down the circus internet, but actually said something smart:
The volume-weighted average price (VWAP) is calculated by dividing the total dollar amount traded for a security over a specific time period by the total volume traded during that same period. This means that prices at which larger volumes were traded have a greater impact on the VWAP calculation than prices with smaller volumes.
To calculate VWAP accurately, it is important to consider the volume distribution over the trading day. Historically, volume is not evenly distributed throughout the day – there are typically periods of higher and lower trading activity.
Many trading algorithms account for this by using historical volume profiles to predict the expected volume distribution over the upcoming trading day. The algorithm then slices the total order into smaller “child orders” that are released at predetermined times based on the forecasted volume distribution.
For example, if 17% of the day’s total volume historically trades in the first hour, the algorithm would aim to execute 17% of the total order during that first hour period.
Get your hands on historical volume profiles and you have a solid start. VWAP algos are commoditized and rest on that research so it shouldn’t be hard to track down.
The quant way
You can use tick data to compute realized variance for each hour and divide by the sum of all the variances for the day to see the proportion by interval. You can use many days data as well as many names to get a cross-sectional perspective.
You will need to treat the period from the prior close to the open in some coherent manner as well. Like you could take the point-to-point variance from the previous close to open divided by the close to close variance over many samples and names and then you can make a statement like “25% of the variance happens overnight.”
That means the remaining hourly variances are then divided by a variance of only .75 of the expected daily variance. Over many days of doing this you will likely get a strong sense of when on average half a day’s variance has transpired.
Extra thoughts
Computing tick vols is a quant rabbit hole of its own. When you come across the words “bid-ask bounce” and “volatility signature plot” you are reading the right stuff.
I’m not a quant researcher. I’m a hacker. I throw numbers in spreadsheets or if I’m really ambitious Python, and turn the crank until I see the shape of the problem. So my methodology above is a zoomed out answer but once you make contact with data the specific details will not go smoothly. Nature of the beast. But the approach is directionally correct you just have to savor the data-wrangling gruel. For example, how many data points are enough? I don’t know — keep adding more until the variations in proportions seem to stabilize at some quantity.
An instinct one develops with enough practice is to know whether your cobbled-together “tape and twine” analysis has a rigor that is proportional to required precision of your use-case. If whatever I’m doing is going to break because I don’t truly understand what “degrees of freedom” means then I just need enough taste to know that I should get a quant’s help.
Discerning how rigorous you need to be is part of being an efficient resource allocator. How much time do you spend on pricing vs execution vs figuring out how to hedge less vs exploring names like not AAPL or other high volume names where Citadel & SIG’s market-makers are trading from the cockpit of F-22s?
GME share price started the month around $11. On Friday May 10th, it closed $17.46. Monday it was about 80% to $31. Tuesday it climbed >50% closing at $48.75 before it would give back over half its gains just as quickly.
In a twitter thread @DeepDishEnjoyer, a former market-maker, called attention to what happened with the July expiry $10 strike put — despite a huge rally the put went up in value. Obviously implied volatility exploded.
Let’s follow along in the thread:
This is quite odd from a first principles perspective. GME closed 17 handle on Friday. Today it meme squeezed up because of Roaring Kitty. A basic model is: it continues meme’ing – then these puts expire worthless or the meme ends and we go back to where we were at at Friday. But note that you could have sold these puts at 75 cents today even though they closed in the 50s on Friday!!!! They should be actually be worth *less* since there is no state of the world where downside vol increased.
He continues:
That’s easily anywhere from 20-40 cents of EV on these puts. And indeed that’s where these puts landed now. So why does it happen? Well, market makers don’t pay a large amount of attention to the wings of their vol surface. ATM implied vol got correctly bid, but they moved the…rest of the surface in parallel EVEN THOUGH THAT MAKES NO SENSE IN A SCENARIO WHERE A STOCK MEME GAPPED UP. Again, vol follows fairly two discrete paths that are intimately tied to stock price – vol is high when the stock is memeing, vol necessarily dies down when it stops.
At the money implied vol should increase. But the strike vol of the 10 strike put should not be massively increasing as the probability of going *below* 10 has not increased today from yesterday, while the options market is implying it has.
So did the IV on those puts go up “too much”?
Settle in. Lots to discuss.
I used the price chart of the put to price the options with a Black Scholes European-style calculator (the American/European thing isn’t important for this).
We start with May 10th just to establish the first elevated IV before stepping through the insanity of the May 13th morning.
It’s a bit hand-wavey since I didn’t know where the spot price was with every corresponding put price on that Monday morning. I assume the put price surged and eased while the spot price remains at $31. The illustration will be valid even if the exact numbers aren’t.
The put price on May 13
For the next section, keep in mind that N(d2) represents probability of option expiring in-the-money.
Stepping through the option prices…
@DeepDishEnjoyer said at $.75 the put implied an even higher chance of going in the money with the stock at $31 than it did when the stock was $17.50.
That checks out in the option model.
It also reflects experienced intuition by DeepDishEnjoyer because I doubt he manually computed N(d2).
The option beginner could have exclaimed “the implied probability isn’t higher — the delta of the put went from .08 to .04!” If you’ve been at the moontower for awhile you understand in high volatility names delta does not equal probability (if you are a new reader then I point you to a top-5 most read post: Lessons From The .50 Delta Option).
When the vol eases back to 175%, still higher than the previous day but off the high, the put’s probability falls to 14% (and the delta falls meagerly from .04 to .03).
Our twitter friend used a sense of implied probability to conclude that the put price expanded too much. And because he says:
there’s easily anywhere from 20-40 cents of EV on these puts. And indeed that’s where these puts landed now
I can infer that while he thought the $.75 price was too high, he may not have a strong opinion on the $.40 price. A price that still represents a much higher IV (175%) vs Friday (112%).
Smacks of a lot of experience. It was also a slightly different way than I would have thought about it.
How my instincts work in such situations
My reflex is also to think in terms of probability. However, I don’t reach for an N(d2) calculator.
I look at put spreads. Tradeable odds.
When DeepDishEnjoyer says the $.75 price is too high a probability, he’s collapsing a lot of compiled mental code into a comment. It’s worth unwrapping.
The price of an option reflects the probability of going in the money as well as how far ITM it can go. The divergence of the delta and N(d2) is model-based clue — since the maximum payoff on that put is capped at $10 then the exploding IV is mostly operating on the probability portion.
My native instinct when thinking about probability is to look at the put spreads since verticals are model-free over/under style bets.
When I think “The $10 put is too high” I hear 2 possibilities:
a) The volatility is too high
or
b) There is a slab of put spreads on the surface that are too cheap where you should buy a higher strike put and sell the expensive $10 put. In this case, you believe the probability of finishing in the money for the $10 put is too high, but the implied probability of the stock going back to $10 is too low.
In other words, we get option trades ideas that are in opposition!
If you believe volatility is too high you should consider selling at-the-money options which have more vega and at least locally less exposure to high-order moments. (Since the market is volatile, you might sell straddles, see the stock move, and your options become OTM, leaving you exposed to those higher-order moments anyway.)
If you think the $10 put is too high, and buy a put spread because you think the implied probability of going to $10 is underpriced. But this is a long vol position.
This is the $20 put if you priced it at 206% vol as well.
Notice how the probability of going ITM is 49% despite the strike being 33% out-of-the-money. Again, even though the probability looks high at nearly 50%, the delta is only .17
So how do we parse this?
We agree the $10 put is too high at $.75…do we sell it as the short leg of a put spread offering 1.8 to 1 on the meme situation ending by mid-July?
The price action looks like that $.75 print was fleeting and likely hard to get on. I doubt the market-makers mispriced it so much as recognized that buyers on a Monday morning could be sloppy traders thinking “I’m buying puts because this stock action is dumb” and were directionally aware but not vol aware. Rip the surface up, print the customers, take it back down to a spot that balances a more level-headed meeting price of buyers and sellers.
It’s hard to disagree with DeepDishEnjoyer. The puts were an outright sale. Probably hard to execute in the fleeting window but the point stands.
The way this situation unfolded, the speed of the rally, occurrence over a weekend, and retrace within a few days reminds me of early 2021 when SLV got aped from about $24 to $27 for a hot second.
The vols blew out across the surface (especially the calls) and I had exactly the same response as DeepDishEnjoyer — sell the downside puts.
Unfortunately…
SLV did a great job pricing them. The best you could get on the 27/24 put spread was an even money payout on the stock retracing back to 24. Any “normal” surface would give you pretty nice odds of a stock falling 10% but the surface was telling you that a 10% sell-off was “home”.
The put vols way underperformed the ATM and call vols. The market understood that those puts were trash and didn’t bid them up. Which made the put spreads, the structure you want to buy, a well-priced risk/reward. Nothing to see here.
The up move in SLV was not as extreme as GME. The vol expansion was only a doubling from about 35 to 70. So those OTM puts weren’t suddenly more expensive than they were pre-move. They just weren’t down as much as you’d expect.
If the stock went back down you would have lost on an unhedged basis. If were hedged then you risk the stock rallying further. And then if you did hedge and the stock fell what delta would you want to be short on? The p/l from a well-priced option trade is just path noise with no compensation.
Here’s a scenario any experienced option trader will relate to:
The stock sells off moderately, the vol comes in, which pushes that strike further OTM and the strike vol rolls up the skew curve as the option goes from say 20 delta to 5 delta despite becoming closer in moneyness. You’ll win on this move, but not as much as you’d like, and if you decide to cover the teeny put when you cover your stock shares you’ll pay a small exit tax on the way out. None of this will have felt worth the brain damage because the option market got it right from the start.
[There was a fleeting moment of edge in all this — there was a window of call buying at over 110% after the open that later settled in to being 90% IV for the next few days. If you missed that window, sure you could have sold 90% vol and thought that was high but you’re basically trading at fair value because there was liquid flow at both sides of that level.
Note the similarity to the GME puts. A fleeting window in the am before options settle into fair. The lesson — only trade a fast market on the open if you want to be a hero and willing to risk being a donkey. Unfortunately, getting filled is not a good sign. If you’d prefer a “fairer” execution you should wait.]
Commodity markets as teachers
I went for a hike during that SLV week with friend who runs a commodity vol fund. We had this moment:
“You wanted to buy put spreads and passed too?!”
We had the same instincts. And the same conclusion. Sell the puts, doh, they don’t look expensive compared to the rest of the surface, dammit, I hate this place.
We joked about how anyone who has ever traded nat gas has these same instincts. It can be April, gas futures for the upcoming Winter could be $8 and no matter which put spread you try to buy to bet gas goes right back to $3 by expiry pays no more than 3-to-1. If you have no frame of reference for odds…imagine being paid only 3-to-1 on a 63% selloff.
I’m looking at Jan25 options in ARKK right now. The 23/17 put spread costs about $.20 with the stock at $45. This spread can be worth $6. You’re getting 29-to-1 on a 63% selloff.
The other joke we made is that in commodities you find these regimes where wingy options just don’t change in price unless insanity happens. Your model says the option has a 5d but the experience is they behave on a 0 delta. This sound ridiculous until you watch people blow out because they have this wrong (nat gas is full of stories of people getting rinsed owning puts on massive selloffs including a large mm).
As a trader, when you see a crazy situation like a meme-stock, it’s useful to ask yourself — what market regularly has this behavior? Is it a market with lots of volume, a centralized/transparent order book, and 20+ years of institutionalized tacit knowledge of how to price options on such weirdness? Nat gas says “check, check and check”.
When a meme stock squeezes, does JANE SIGCIT just yell turn off “equity sheets run gas skew in GME?”
The truth is the gas market is very smart. The options are priced in such a way that the path is highly respected. The OTM calls are jacked, because if we see H gas trade $10, the straddle will go nuclear.
Why? Because it has to balance 2 opposing forces.
It’s not clear how high the price can go in a true squeeze or shortage
The MOST likely scenario is the price collapses back to $3 or $4.
Let me repeat how gnarly this is.
The price has an unbounded upside, but it will most likely end up in the $3-$4 range.
Try to think of a strategy to trade that.
Good luck.
Wanna trade verticals? You will find they all point right back to the $3 to $4 range.
Upside butterflies which are the spread of call spreads (that’s not a typo…that’s what a fly is…a spread of spreads. Prove it to yourself with a pencil and paper) are zeros.
As a matter of prospecting, you can expect that each time a market starts “meme’ing” the playbooks become more obvious for the surface setters. That said, market-makers are exceptional pattern-matchers so if you have a reason why a familiar setup will have a different endpoint, you’ll be able to find great prices. But if you have the consensus “this thing is headed back home” view know that the prices already reflect that. You’re just tossing coins for even money.
We’re going to come back to silver again in a moment.
In all this writing, I hope the message is coming across — you should not touch options if you have a directional opinion but not a vol opinion.
On Monday, we held the moontower.ai community zoom. We talked about the newly released Moontower Mission Plan series. The core goal of the series is to walk a user through the process of developing a volatility opinion (or “axe” as in “axe to grind” — trading lingo).
As we walked through the steps, I found that SLV near-dated downside (ie 1 month) looked like a sale.
The IV was elevated and the term structure strongly descending so we proposed selling near-dated…
…but then we check the VRP (volatility risk premium) to see how the IV looked compared to recent realized vol and found a healthy amount of carry.
So we like selling near-dated SLV vol.
Now SLV has been rallying along with GLD. This thread by @SantiagoAuFund makes the case for a tactical short directional position in silver. The sentiment and COT positioning reasons are the ones that resonate most with me.
[Plus the fact that he’s being attacked for being bearish. I like when a trade offends people — if everyone is bulled up then the market is more likely to compensate the sellers since that’s whose service is needed. And if positioning indicates that speculators are already very long, then that’s embedded in the current price plus there’s less people left to buy. I hold no long term view on silver — I just like the tactical idea.]
Santiago expressed his bet via buying puts. This is where we differ. SLV vol looks like a sale so I want to express the bearish directional view in a short vol way. I also prefer simplicity. So I’d limit the trade expressions to:
Selling ATM or ITM callsThe skew in the one month 25d puts according to our metrics is in the 47th percentile so it’s pretty fair therefore I don’t feel ripped off selling the ITM calls. (You could also sell the OTM puts and short the stock on a 1-1 ratio. It’s synthetically the same trade.)
Sell straddles where the call is ITM.Same trade as the earlier one, but the initial delta is not as short (so if your directional conviction isn’t strong. Also if you sold OTM puts and hedge with half the number of shares this is synthetically an ITM straddle. The shares turn 1/2 the puts into synthetic calls. So if you sold 10 OTM puts and 500 shares your synthetically short 5 ITM straddles. Put-call parity is fun.)
You could sell the calls and cap your risk by buying an OTM call.This is a short call spread. Since you are buying a higher strike call, your initial vega will not be as short. The wider the call spread the more the risk looks like a naked short call and the more short vol you are expressing (not to mention shorter deltas).
A more advanced trade could be to buy 1×2 put spreadsYou could buy an ITM put to sell 2 OTM puts. You can find the strikes that dial in the desired initial delta and vega. But you can also see that this is the equivalent of buying a put spread and selling an extra OTM put. Or selling a straddle and buying a single OTM option to hedge. Options are Legos to build the structures you want, but just as a chess player chunks positions into familiar patterns, options can all be reduced to a combination of straddles and verticals (if we stick to a single expiry).
Ok, that’s enough for today.
Also, disclaim disclaim disclaim. You own your own decisions. I’m just saying what I see not recommending you do anything.
An option trader pinged me about a trade between a correlated pair of names whose IV ratio was trading at an extreme level compared to the ratio of realized volatilities that the pair has experienced in the past.
This trader is experienced. He understood that pitting vanilla options against one another invites path dependence. It’s worth spelling that out with a demonstration:
Imagine both assets are trading for $100 so you buy the 100 strike straddle in asset A and short the 100 strike straddle in asset B. Once these assets start bouncing around the moneyness of the straddle positions will get out of sync. After a week if both assets realize the same volatility but the path of A means it’s up 5% and the path of B means its up only 2% then you will have more gamma and theta in B because the straddle is closer to at-the-money (ATM). The further you get from a strike the more your exposure “goes away”. Far OTM options spit off smaller greeks and are less sensitive to changes in underlying price or volatility.
Let’s get to the question.
He was theta-weighting the trade instead of vega-weighting the trade. He wanted to know if I would do the same.
I’ll give examples of how each approach will end up weighting the legs, how I’d weight the trade, how to map weightings to the nature of a relationship, and even what greeks depend on.
By the time you finish this post, you will be able to understand the risks of different weightings and how to compute weightings in your head knowing nothing else except spot prices and ATM vols.
Let’s start with definitions.
Delta
Change in option price for a $1 change in the stock price
If an option has a .50 delta and the stock increases by $1, the option value increases by $.50
If it was a put option the delta would be negative. If the option has a -.50 delta and the stock increases by $1, the option falls by $.50. If the stock had fallen by $1 then the option increases in value by $.50
Vega
Change in option price for a 1 point change in the implied volatility
If an option has .20 of vega than a 1 point increase in implied vol, for example from 15% to 16%, the value of the option increases by $.20
If implied volatility fell from 15% to 14%, the option loses $.20
Gamma
The change in the delta for a $1 change in the stock price
If an option has .05 gamma and .50 delta and the option goes $1 more in-the-money then the option delta increases from .50 to .55. The option is becoming more sensitive to the stock price. As an option goes far in-the-money its delta continues to increase because of gamma until it approaches 1.00. At that point the option is so far in-the-money it moves 1-to-1 with the stock price.
If our .50 delta option with .05 gamma falls $1 out-of-the money its delta falls to .45. It becomes less sensitive to the stock price on the subsequent move. If the option continues to fall further out-of-the-money, its delta will fall to zero and changes in the stock price will have no impact on the option value. It is so far out-of-the-money it’s likely worthless.
Theta
The amount an option price decays when 1 day elapses
A key observation which harkens back to the path-dependance demonstration:
Greeks, ie option sensitivities, are a single snapshot in time.
They change if any of the inputs change — volatility, time to expiry, interest rates/divs, or moneyness (ie the distance of the stock price from the strike price).
This is important because when we place a pair trade (long one option and short another on different names) we initialize it by trying to do it in a vega or theta neutral way. We aren’t trying to make a statement about the general implied vol, but the relationship of the implied vols to one another.
Getting back to the reader’s question…do we initialize neutrality with vega or theta?
The answer depends on what you are trying to capture when you bet on the relationship of the implied vols.
What is it about the relationship that you are trying to make a statement about?
Do you believe the implied vols should trade at a certain spread to each other?
For example, stock A’s implied volatility is typically 5 points higher than stock B, but they are both trading for the same volatility so you want to buy a straddle on A and short a straddle on B. How do you weight that trade?
Do you believe the implied vols should trade at a certain ratio to each other?
For example, you believe stock A should trade at a 50% higher volatility then stock B. If both are trading for 10% volatility, you want to buy straddles on A and short straddles on B. How do you size those trades?
There can be a world of difference between a spread vs ratio relationship.
If stock A is 20% volatility and stock B is 10% volatility the ratio is 2 and spread is 10 points.
If both volatilities double then the ratio is constant but the spread is now 20 points!
If you weighted the trade to bet on the ratio your p/l is 0. If you weighted the trade assuming the spread would stay fixed, your pair trade is now spitting off a bunch of p/l.
The easiest way to build intuition for this is a toy example.
Consider 2 stocks, HighVol and LowVol. They are both $100 and we are going to initiate a pair trade in a 6-month options.
Regardless of the volatility, the options on each name have the same vega.
HighVol options, which are twice the volatility of LowVol, have twice the theta and half the gamma.
Intuition:
theta: An option that has 2x the volatility, all else equal, is worth 2x the premium of the lower vol option. It has 2x the amount of theta to decay to zero.
gamma: A $1 move is twice as significant to LowVol than HighVol. Just like a 1% move in SPY is more meaningful than a 1% move in TSLA.
Higher implied vols mean bigger thetas and smaller gammas
P/L under both weighting schemes if volatility doubles
Vega-weighting
If you vega-weight the pair trade you will trade the same amount of options in each name. Why?
If you short 100 contracts of HighVol your net vega will be -2810.
-100 x .281 x 100 share multiplier
If you buy 100 contracts of LowVol your net vega will be +2820
+100 x .282 x 100 share multiplier
Net vega = -2810 + 2820 = 10 which rounds to zero. If the vol in both names goes up by 1 point you make $10 which is 1/10 of a penny on 100 option contracts. Less than the commission. Mark it zero.
We’ll just round the vega positions to long and short 2800 for the 2 legs of the trade.
What happens when vol doubles?
Notice that vega per option doesn’t really change. Computing the p/l is straight forward.
Your long option position in LowVol increased by 15 vol points (15% to 30%).
P/L on long options = 15 points x 2800 = $42,000
P/L on short options = 30 points x -2800 = -$84,000
Total p/l for pairs trade = -$42,000
If you vega-weight a trade, you are exposed to the spread! The ratio stayed the same but you experienced p/l. This weighting was not a bet on the ratio!
Theta-weighting
Let’s buy LowVol and short HighVol again but this time weight the legs by theta. Remember, LowVol has half the theta as HighVol so to be theta-neutral we must buy 2x as many options in LowVol.
Let’s buy 200 options in LowVol vs shorting 100 option in HighVol.
We are theta-neutral, but what’s our net vega?
Vega in LowVol = 200 contracts x .28 x 100 multiplier = 5,600 vega
Vega in HighVol = 100 contracts x -.28 x 100 multiplier = -2,800 vega
Net vega = +2,800
A theta-neutral weighting means we are long vol.
Once again let’s shock the vol but keep the ratio constant.
If LowVol goes from 15% to 30% we make 15 vol points x 5,600 = $84,000
This perfectly offsets the $84,000 loss we’ll experience when we ride a short 2,800 vega position in HighVol up 30 points as vol doubles form 30% to 60%.
Theta weighting neutralizes our position to the ratio, but it is exposed to the spread!
Consolidating what we know
If we balance thetas:
our positions will have a net vega
we are hedged against the ratio of the vols but not the spread
If we balance vegas:
our positions will have a net theta
we are hedged against the spread but not the ratio of the vols
How would I weight an option pair trade?
I generally look at trades as ratios. Why?
Because they are not level-dependent.
If the absolute level of vol is in a tight range then the spread will be stable. For example if you trade WTI crude options against Brent crude the vols are similar. If you buy 5,000 vega in WTI at 29 vol and hedge by shorting 5,000 vega in Brent at 30 vol you are vega-weighting the pair. And that will suffice for small changes in volatility. The ratio will move around a bit, but for the most part the vol spread will be pretty fixed and you’re roughly hedged so long as that’s true.
But over wide changes in volatility, the ratio is more likely to hold. If there are 2 names that are 10% and 20% vol respectively and vol roofs, I don’t expect that we’ll find these names trading at a 10 point spread like 60% vs 70%.
They won’t be trading 60% and 120% to keep the ratio constant either. But there will be less error in assuming that then vega-weighting as if the spread will stay constant.
Once a grenade goes off, path dependence is likely to swamp much of the error around the edges as you will see your vegas grow and shrink as the spot moves closer or further from your strikes as realized vol starts interacting with the implied vols.
Neither weighting is a panacea for “Am I fully hedged?”
You should look at the history of a relationship to see if the ratio or spread appears to govern the bungee cord between the 2 names but my default is theta-weighting which implies more trust in the ratio.
Just remember:
if you are betting on the ratio, use theta-weighting
if you are betting on the spread, use vega-weighting
The vega of ATM options
Holding DTE constant, we saw that gamma and theta depend on the vol level.
You may also have noticed that vega didn’t.
The 15%, 30%, and 60% vol options all had about the same vega. That reality is why we used an equal weight for the legs of the trade when we vega-weighted.
So what does vega depend on?
This is neat — ATM vega depends only on the spot price and DTE. We are holding DTE constant.
[Note: When I use ATM here I’m technically referring to ATF or at-the-forward but I’ll just say ATM which is more familiar to most]
So ATM vega only depends on the spot price. If you double the spot price you double the vega.
The proof of this can be seen easily from the approximation of the ATF straddle:
If I re-write that, it’s clear:
Straddle = σ x (.8 * S * √t)
Remember vega is change in option price per 1 point change in volatility.
A 1 point increase in σ changes the straddle by .8 * S * √t
Ignoring time ‘til expiry, the ATM vega is strictly a function of spot price!
If we vega-weight a pairs trade and Stock A is half the price of Stock B you will need to buy 2x as many options on A. In the examples we did above, both stocks were the same price.
Final recap
Holding DTE constant:
ATM vega depend only on spot price.Even if a pair has different vols, to vega weight a pairs trade simply weight by the ratio of the prices. This is a bet on the vol spread.
Thetas are proportional to vol levels.To theta weight a trade, weight by the ratio of the vols. This is a bet on vol ratio.
If a known event such as as a stock’s earnings date announcement we expect the market to assign extra volatility to any expirations which include that event.
Option traders will decompose such an implied volatility into:
A single day event vol or expected move size
The typical vol or move size for a regular day
If you were looking at a student’s grade in chemistry you know it was the average of the tests. But if the final exam has a bulk of the weight and the remaining tests were equally weighted you have no way of backing out with the final’s weight was.
The option’s trader faces a similar problem. How much of the implied volatility is coming from the market’s estimate of the event move size?
The best a trader can do is tinker with assumptions for the earnings or event move and then see what that implies for a typical trading day.
An “expected move size” corresponds to the value of a straddle. By converting straddles into an implied volatility for that single day, we can back out the volatility that is equally assigned to the remaining trading days until expiry.
The larger estimated event move, the lower the implied vol must be for the remaining days and vice versa.
Application: “Renting” The Straddle
Imagine a 30 day option on XYZ stock. XYZ is announcing earnings the morning of the option expiry date and you expect that the earnings move will be 4%*. Therefore you expect the straddle to be worth 4% right before earnings are announced or about 80% volatility (see straddle approximation calculator)
But what if it’s worth 4% today?
A 4% straddle with 30 days until expiry corresponds to an implied volatility of 17.5%
We expect the straddle to be worth 4% of the stock price just before the last trading day. A 4% straddle corresponds to an 80% volatility with 1 DTE
Therefore, the implied volatility must increase from 17.5% to 80% between now and expiration. This increase in implied volatility will exactly offset the theoretical option theta if the straddle has remained a constant 4% of the stock price over the course of the month!
If a trader knew this, they could buy the straddle today, hedge the gamma and then sell the straddle before earnings is announced. This kind of trade is known as “renting the straddle”.
This example is idealized. The trader got to “rent a straddle” implying zero volatility for all the days preceding earnings. It was free gamma. The example is meant to illustrate the idea that implied volatility is not distributed evenly across all days and by “extracting” volatility ascribed to events you can make better comparisons cross-asset.
*Perhaps by looking at how the name has moved on prior earnings dates. Estimating move sizes is an active area of research for practitioners. You can think of the problem inversely – you can try to fit the event size to your estimate of a fair trading day volatility. It is common to use this calculator in both directions.
